Displaying as Temporalizing

Abstract

A particularly appealing feature of intuitionistic propositional logic, IPL, is that it may be regarded as the logic of cumulative research, see [12]. It is sound and complete with respect to the class of all non-empty sets I of information states which are quasi-ordered by a relation ⊑ of ‘possible expansion’ of these states, and in which atomic formulas established at a certain state are also verified at every possible expansion of that state. There are thus three constraints which are imposed on the basic picture of information states related by ⊑ : (i) the persistence (alias heredity) of atomic information, (ii) the reflexivity, and (iii) the transitivity of ⊑ . The persistence of every intuitionistic formula emerges as the combined effect of (i) and (iii). Although a Kripke frame, that is, a binary relation over a non-empty set, admittedly provides an extremely simple model of information dynamics, and, moreover, each of the conditions (i) — (iii), as well as their combinations, may be of value for reasoning about certain varieties of scientific inquiry, it is nevertheless interesting and reasonable to consider giving up all or some of these conditions. Evidently, conceiving of information progress as a steady expansion of previously acquired insights is extremely idealized and the basic model of such a progress should leave room for incorporating revisions, contractions, and merges of information as well. If persistence is given up, ⊑ can no longer be understood as a relation of possible expansion. This reading, however, may be replaced by more generally thinking of ⊑ as describing a possible development of information states. Development thus need not imply the persistence of information.